We have already mentioned the indirect means that must be employed to obtain distances to OB associations. In contrast, the familiar open cluster of the Hyades is one of the few stellar groups close enough that its distance follows from velocity measurements alone. The proper motion vectors of the stars all converge to a single point, indicating that the cluster is receding. If 6 is the system's present angular diameter, the proper motions yield 6, the rate at which this diameter is shrinking. For small 6, the fractional rate of shrinking, 6/6, is also equal to Vr/d. Here, Vr is the common radial velocity of the stars at distance d. Once the velocity is determined from Doppler shifts of the spectral lines, this moving-cluster method directly gives d, which is 41 pc in the present case.
The actual value of the Hyades distance is not as important as the role of the moving-cluster method in astronomical calibration. Within the Hyades, knowing the cluster distance allows one to assign luminosities to all members with measured apparent magnitudes. Since many of these stars are on the main sequence, this assignment, together with spectroscopic temperature determinations, establishes the ZAMS empirically over a finite range of L* and Teff. Turning to other open clusters, one can now apply the technique of spectroscopic parallax described in § 4.3. That is, we vertically slide each diagram of mV versus spectral type until it matches the Hyades, thereby both establishing the cluster distance and completing the calibration of the main sequence itself. Such main-sequence fitting is the basis of the ZAMS represented by the theoretical curves in Figures 1.15 and 1.18. The distances provided by the moving-cluster method and spectroscopic parallax form the lowest rungs of the cosmic distance ladder. To go beyond our Galaxy, we must utilize other techniques - including observations of pulsating stars and supernovae - to bootstrap our way outward. At each step, however, the most reliable measurements are relative ones, so that even the greatest cosmological distances rest ultimately on those few established kinematically for nearby open clusters.
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